53 



First let me call your attention to the fact that there are several lines of 

 evidence which bear on this picture. In the first place you have theoretical cal- 

 culations, such as Dr. Platzman was telling us about yesterday. Then there are 

 experimental results. There are physical experiments and chemical experi- 

 ments, and these all bear on the spatial distribution. We have thought about all 

 of these things. 



First let us review. Let's mention the theoretical evidence, and go back to 

 the primary event in which there is only one electron. I started thinking about 

 this several years ago, and so I was quite interested in the problem that Dr. 

 Platzman was discussing yesterday. I didn't want to do such an elaborate cal- 

 culation, and yet I wanted to get an approximate result. As a matter of fact, I 

 must say at that time I thought the electron got quite far away, and if you re- 

 member a paper (4) that Dr. Burton and I wrote, we were discussing electron 

 capture as a competition of various processes. I thought the electron certainly 

 got free of the coulomb field, and I just wanted to get a rough estimate of how 

 far it went, and so I looked in the literature and got experimental data on elec- 

 tron scattering and capture. Bruche (5) had reported scattering data and Bailey 

 and Duncanson (6) had reported energy loss data for slow electrons in water va- 

 por. Doubt has been cast on the validity of these data even for the gas phase. 

 I used it anyway and calculated the distance that the electron would get away, 

 saying that it would move in such a way that r^ = nL^, where r is the distance 

 of the electron with respect to its parent ion, L is the scattering mean free 

 path, and n is the number of collisions which have occurred. For n we can take 

 n = vt/L where v is the velocity and t is the time. If the coulombic energy is 

 neglected, the only change in electron energy is due to inelastic collisions, and 

 we can say - dE = \ E, where \ is the fraction of energy lost per collision. 



dn 

 Substitution for n gives 



dE _ X 



E 



dr 2 " L 2 



and integration, for constant parameters X and L gives 



E = E exp (-Xr2 / L 2 ) 



if the electron starts with E = 10 ev, it gets down to E = l/40 ev (thermal en- 

 ergy) when 



r z _ L 2 In 400 6L 2 



For L = 2 A, X = 0. 04: ( r z ) 2 = 24 A 



th 

 This calculation is obviously inconsistent, since at 24 A separation the 

 coulombic energy is much higher than thermal energy. Samuel and I (7) have 

 made a similar classical calculation in which we took into account the cou- 

 lombic field, and, of course, the electron does not get away quite as far in this 

 case. 



ONSAGER: This calculation is classical in what respect? 



MAGEE: The electron is taken as a point charge, and I will remind you of 

 a fact that Dr. Platzman mentioned yesterday. The electron starts off with 



